Ashers Bakery Company will appeal to the UK Supreme Court in central London during a two-day hearing scheduled for October.
Daniel McArthur, the general manager of Ashers, said: “The fact that the Supreme Court is willing to hear arguments is very encouraging and reflects the importance of the issues and the high-profile nature of the case.”
The bakery was approached in May 2014 by gay rights activist Gareth Lee, who placed an order for a cake with the slogan “Support Gay Marriage”.
Ashers initially accepted the order. However, it contacted Mr Lee two days later to say staff could not proceed with the order due to the message requested.
During the first court case, district judge Isobel Brownlie ruled the law could not be dictated by religious beliefs and ordered Ashers to pay £500 in damages.
Representing Ashers, Daniel McArthur and his wife, Amy, took their case to the Court of Appeal in October last year, but were unsuccessful.
Launching an appeal, Ashers argued it had not objected to Mr Lee’s sexuality, rather the message he had requested for the cake. They argued it was inconsistent with their deeply held religious beliefs.
Mr Lee, who is a member of the LGBT advocacy group Queer Space, took legal action against Ashers with the support of Northern Ireland’s Equality Commission.